Preheat oven to 425°F (220°C). On a large baking sheet, toss the cubed potatoes with 2 tbsp olive oil, 1 tsp salt, and 1/2 tsp pepper. Spread into a single layer and roast for 25-30 minutes, flipping halfway, until golden-brown and crispy with charred edges.

While potatoes roast, pat the chicken breasts completely dry and season both sides with salt and pepper. Heat 1 tbsp olive oil and 1 tbsp butter in a large skillet over medium-high heat. Sear the chicken for 5-7 minutes per side until golden-brown and cooked through (165°F / 74°C). Remove chicken and set aside.

Reduce skillet heat to medium. Add minced garlic and sauté for 30 seconds until fragrant. Deglaze the pan with chicken broth, scraping up any browned bits. Stir in the heavy cream and simmer for 3-5 minutes until the sauce thickens.

Stir the fresh parsley and thyme into the sauce. Season with salt and pepper to taste. Return the chicken to the skillet, spooning sauce over the top. Serve immediately with the crispy roasted potatoes, garnished with extra parsley and freshly ground black pepper.